{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:WPDJEYB7U2R7OLHFPYGPTE355S","short_pith_number":"pith:WPDJEYB7","canonical_record":{"source":{"id":"math-ph/0508052","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-08-25T22:21:00Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"5f69bc69950dfc03412cdcc6dd26ae05d8518f3be55f8d023077886d19bbf28b","abstract_canon_sha256":"c6ac038fb74db3a4ed5b291dc497209f8b862e656db0786d03c47da8fb3a9551"},"schema_version":"1.0"},"canonical_sha256":"b3c692603fa6a3f72ce57e0cf9937decbde10901dae983611654066c5f294f44","source":{"kind":"arxiv","id":"math-ph/0508052","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0508052","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0508052v1","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0508052","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"WPDJEYB7U2R7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"WPDJEYB7U2R7OLHF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"WPDJEYB7","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:WPDJEYB7U2R7OLHFPYGPTE355S","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0508052","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-08-25T22:21:00Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"5f69bc69950dfc03412cdcc6dd26ae05d8518f3be55f8d023077886d19bbf28b","abstract_canon_sha256":"c6ac038fb74db3a4ed5b291dc497209f8b862e656db0786d03c47da8fb3a9551"},"schema_version":"1.0"},"canonical_sha256":"b3c692603fa6a3f72ce57e0cf9937decbde10901dae983611654066c5f294f44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:33.092123Z","signature_b64":"n0Fp5VMgJrwVrreMo9sAZqDOfV7ZxBWlXvZYCtBKO+5g65EfmHideVoKyM8WKdz4DMSFG2fzmuVV1K+/p6PvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3c692603fa6a3f72ce57e0cf9937decbde10901dae983611654066c5f294f44","last_reissued_at":"2026-05-18T01:38:33.091460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:33.091460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0508052","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IqfmRx4UXQ5OQTP62UYm9Li/N8otXdw49HsGLmVkwOX3WRZPQf7aUX/FhBzm7Ptbli7Yecf9YHeaHwIUa/qHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:42.995794Z"},"content_sha256":"c09efeb778f8af699ea616b0eacdbb94c7cf2e10da0d4110e2c54f03d471de9a","schema_version":"1.0","event_id":"sha256:c09efeb778f8af699ea616b0eacdbb94c7cf2e10da0d4110e2c54f03d471de9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:WPDJEYB7U2R7OLHFPYGPTE355S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Carleman estimates and absence of embedded eigenvalues","license":"","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Daniel Tataru, Herbert Koch","submitted_at":"2005-08-25T22:21:00Z","abstract_excerpt":"Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0508052","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IN1TtVNMszwweClFpZ3hiD8L5jRnbHN3CIBDCJDcZDEf9+etXfSkbkVf9KKEG6Bf5nCUxwAgKDRRPSb9DDULAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:42.996129Z"},"content_sha256":"84680faffe6e83d9f77b2ecf1a4dad4b8cbb3491ffa669c1c3d9dd0197497375","schema_version":"1.0","event_id":"sha256:84680faffe6e83d9f77b2ecf1a4dad4b8cbb3491ffa669c1c3d9dd0197497375"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPDJEYB7U2R7OLHFPYGPTE355S/bundle.json","state_url":"https://pith.science/pith/WPDJEYB7U2R7OLHFPYGPTE355S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPDJEYB7U2R7OLHFPYGPTE355S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T04:15:42Z","links":{"resolver":"https://pith.science/pith/WPDJEYB7U2R7OLHFPYGPTE355S","bundle":"https://pith.science/pith/WPDJEYB7U2R7OLHFPYGPTE355S/bundle.json","state":"https://pith.science/pith/WPDJEYB7U2R7OLHFPYGPTE355S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPDJEYB7U2R7OLHFPYGPTE355S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:WPDJEYB7U2R7OLHFPYGPTE355S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c6ac038fb74db3a4ed5b291dc497209f8b862e656db0786d03c47da8fb3a9551","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-08-25T22:21:00Z","title_canon_sha256":"5f69bc69950dfc03412cdcc6dd26ae05d8518f3be55f8d023077886d19bbf28b"},"schema_version":"1.0","source":{"id":"math-ph/0508052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0508052","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0508052v1","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0508052","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"WPDJEYB7U2R7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"WPDJEYB7U2R7OLHF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"WPDJEYB7","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:84680faffe6e83d9f77b2ecf1a4dad4b8cbb3491ffa669c1c3d9dd0197497375","target":"graph","created_at":"2026-05-18T01:38:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.","authors_text":"Daniel Tataru, Herbert Koch","cross_cats":["math.AP","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-08-25T22:21:00Z","title":"Carleman estimates and absence of embedded eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0508052","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c09efeb778f8af699ea616b0eacdbb94c7cf2e10da0d4110e2c54f03d471de9a","target":"record","created_at":"2026-05-18T01:38:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c6ac038fb74db3a4ed5b291dc497209f8b862e656db0786d03c47da8fb3a9551","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-08-25T22:21:00Z","title_canon_sha256":"5f69bc69950dfc03412cdcc6dd26ae05d8518f3be55f8d023077886d19bbf28b"},"schema_version":"1.0","source":{"id":"math-ph/0508052","kind":"arxiv","version":1}},"canonical_sha256":"b3c692603fa6a3f72ce57e0cf9937decbde10901dae983611654066c5f294f44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3c692603fa6a3f72ce57e0cf9937decbde10901dae983611654066c5f294f44","first_computed_at":"2026-05-18T01:38:33.091460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:33.091460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0Fp5VMgJrwVrreMo9sAZqDOfV7ZxBWlXvZYCtBKO+5g65EfmHideVoKyM8WKdz4DMSFG2fzmuVV1K+/p6PvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:33.092123Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0508052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c09efeb778f8af699ea616b0eacdbb94c7cf2e10da0d4110e2c54f03d471de9a","sha256:84680faffe6e83d9f77b2ecf1a4dad4b8cbb3491ffa669c1c3d9dd0197497375"],"state_sha256":"704b431a920a7a4e50c472cbfeaa13a396e61e361aa1a51390c2475311a00718"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vMKkKIhoumFUgcigIfuCc9lrVsi1tvy34ZLm52JpzV6gKWUkpeF+OBsEg+otiUKj2GHL46pC66xiETSpXuLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:15:42.998070Z","bundle_sha256":"27eceb575ae4e98143272b19f1ee61bafea08d89bdd56ead6b72c2f59f90bca4"}}